Density, distribution function, quantile function and random
generation for the logistic distribution with parameters
location
and scale
.
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x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
location, scale |
location and scale parameters. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. |
If location
or scale
are omitted, they assume the
default values of 0
and 1
respectively.
The Logistic distribution with location
= m and
scale
= s has distribution function
F(x) = 1 / (1 + exp(-(x-m)/s))
and density
f(x) = 1/s exp((x-m)/s) (1 + exp((x-m)/s))^-2.
It is a long-tailed distribution with mean m and variance π^2 /3 s^2.
dlogis
gives the density,
plogis
gives the distribution function,
qlogis
gives the quantile function, and
rlogis
generates random deviates.
The length of the result is determined by n
for
rlogis
, and is the maximum of the lengths of the
numerical arguments for the other functions.
The numerical arguments other than n
are recycled to the
length of the result. Only the first elements of the logical
arguments are used.
qlogis(p)
is the same as the well known ‘logit’
function, logit(p) = log(p/(1-p)),
and plogis(x)
has consequently been called the ‘inverse logit’.
The distribution function is a rescaled hyperbolic tangent,
plogis(x) == (1+ tanh(x/2))/2
, and it is called a
sigmoid function in contexts such as neural networks.
[dpq]logis
are calculated directly from the definitions.
rlogis
uses inversion.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 2, chapter 23. Wiley, New York.
Distributions for other standard distributions.
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